Corrugated fiberboard boxes are used for storing and carrying items. Some conventional corrugated fiberboard boxes include handles in the form of openings in opposing side walls for receiving a person's hands. The side walls oftentimes each include a single panel of corrugated fiberboard, which limits the amount of weight that the box can support while a person is holding the box by the openings before the single-panel side walls rip or tear from the weight. Sometimes, the side walls each include two panels (i.e., double-layered side walls), which may increase the amount of weight that the box handles can support. However, when the panels in such a conventional box are corrugated, the orientation or direction of the corrugations of the panels is the same (i.e., aligned) for each panel, which can induce tearing along the corrugation direction when the amount of weight is increased. It would therefore be desirable to have a box with improved structural integrity.